{
  "abstract": "Motivated by problems in instanton continuation, we establish geometro-topological selection rules for continuing a Riemannian region into a Lorentzian region through a smooth transverse change of signature. Given a collar-gluing $M=\\overline{M_R} \\cup_{\\mathcal{H}}\\overline{M_L}$ of a smooth manifold $M$ along a hypersurface $\\mathcal{H}$, we show that an admissible signature-changing metric of the form $\\widetilde g=g-fV^\\flat\\otimes V^\\flat$ with $g$ a Riemannian metric, having Riemannian signature on $M_R$ and Lorentzian signature on $M_L$, exists if and only if a relative Euler class obstruction on $\\overline{M_L}$ vanishes. This obstruction combines ordinary Euler characteristics $χ$ in a manner that depends on which components of $\\mathcal{H}$ represent big bangs and which represent big crunches. It also restricts the choice of $M_R$; for example, if $M$ is closed and $\\dim M$ is even, then it requires$χ(\\overline{M_R})=χ(M)$. We also determine and classify the possible compactness types of $\\overline{M_R}$, $\\mathcal{H}$, and $\\overline{M_L}$ occurring in such a collar-gluing construction, and construct explicit signature-changing metrics in each case. Topology change can be entirely contained within the Riemannian region when $M$ is the interior of a compact manifold with boundary.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27136",
  "author_total": 2,
  "authors": [
    {
      "name": "Nathalie E. Rieger"
    },
    {
      "name": "Ödül Tetik"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b09kepkxzaq21.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27136",
  "fulltext_url": null,
  "id": "b09kepkxzaq21",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27136",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "gr-qc"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7214406004",
  "pdf_url": "https://arxiv.org/pdf/2609.27136",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b09kepkxzaq21.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:52Z",
      "native_id": "2609.27136",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27136"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Topological Obstructions to Riemannian-Lorentzian Continuation",
  "title_text": "Topological Obstructions to Riemannian-Lorentzian Continuation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/b09kepkxzaq21",
  "venue": "arXiv",
  "versions": []
}